Does the equation 7x - 4y = 0 represent a direct variation? If so, find the constant of...

Question:

Does the equation 7x - 4y = 0 represent a direct variation? If so, find the constant of variation.

A) yes; {eq}k= \frac{7}{4} {/eq}

B) yes, k= -4

C) No

D) yes; {eq}k= \frac{-7}{4} {/eq}

Direct and Inverse Variation:

Direct Variation:

  • If x varies directly as y then {eq}x=ky {/eq}, where 'k' is a constant of variation.

Inverse Variation:

  • If x varies inversely as y then {eq}x= \dfrac{m}{y} {/eq}, where 'm' is a constant of variation.

Answer and Explanation:

The given equation is:

$$7x - 4y = 0 \\ \text{Subtracting 7x from both sides}: \\ -4y=-7x \\ \text{Dividing both sides by -4}, \\ y= \dfrac{7}{4}x $$

This is of the form {eq}y=kx {/eq}. So this represents a direct variation.

The constant of variation is, {eq}k= \boxed{\mathbf{ \dfrac{7}{4}}} {/eq}.

Therefore, the answer is (A).


Learn more about this topic:

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Solving Equations of Direct Variation

from Algebra I: High School

Chapter 17 / Lesson 9
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